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Stochastic properties and reliability measures of discrete-time semi-Markovian systems

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  • Yi, He
  • Cui, Lirong
  • Shen, Jingyuan
  • Li, Yan

Abstract

In the present paper, a discrete-time semi-Markovian system is studied for both theoretical and practical demands. The state space of a semi-Markov chain is divided into three subsets, namely working state subset, changeable state subset and failure state subset, resulting from applications for this kind of models in degradation analysis on system performances. Performances of changeable states depend on recent evolutions of the system, including the immediate history and future. The Z-transform is used to investigate stochastic properties of the semi-Markovian system and distributions of some sojourn time lengths, based on which, for example, the working period length and failure period length, are discussed. Reliability measures such as reliability, point availability and interval availability are derived for the system. Besides, two new reliability measures, point covering availability and interval covering availability, are discussed for discrete-time semi-Markovian systems for the first time. Preventive maintenance and corrective maintenance from outside of the system are also investigated with respect to related costs. Finally, a numerical example is given to illustrate the results obtained in the paper. Those models and results presented in the paper can be used in reliability, maintainability, supply chain management and other areas.

Suggested Citation

  • Yi, He & Cui, Lirong & Shen, Jingyuan & Li, Yan, 2018. "Stochastic properties and reliability measures of discrete-time semi-Markovian systems," Reliability Engineering and System Safety, Elsevier, vol. 176(C), pages 162-173.
    • Handle: RePEc:eee:reensy:v:176:y:2018:i:c:p:162-173
    DOI: 10.1016/j.ress.2018.04.014
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    References listed on IDEAS

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    Cited by:

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    2. Vahid Andalib & Jyotirmoy Sarkar, 2022. "A System with Two Spare Units, Two Repair Facilities, and Two Types of Repairers," Mathematics, MDPI, vol. 10(6), pages 1-13, March.
    3. Guglielmo D’Amico & Raimondo Manca & Filippo Petroni & Dharmaraja Selvamuthu, 2021. "On the Computation of Some Interval Reliability Indicators for Semi-Markov Systems," Mathematics, MDPI, vol. 9(5), pages 1-23, March.
    4. Yi, He & Cui, Lirong & Balakrishnan, Narayanaswamy, 2021. "New reliability indices for first- and second-order discrete-time aggregated semi-Markov systems with an application to TT&C system," Reliability Engineering and System Safety, Elsevier, vol. 215(C).

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